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The Hermite random field has been introduced as a limit of some weightedHermite variations of the fractional Brownian sheet. In this work we define itas a multiple integral with respect to the standard Brownian sheet andintroduce Wiener integrals with respect to it. As an application we study thewave equation driven by the Hermite sheet. We prove the existence of thesolution and we study the regularity of its sample paths, the existence of thedensity and of its local times. 2000 AMS Classification Numbers: 60F05, 60H05,60G18.

Wiener integrals with respect to the Hermite random field and applications to the wave equation